And Rosta wrote:
>
> It reminds me of the mathematics of biological forms -- e.g. leaf growth
> following fractal patterns, and shoots branching off from stems at
> intervals that follow the fibonacci sequence.

Perhaps you've read Lyle Jenkins' _Biolinguistics_. I have a review
of the book for anyone who's interested.

> If you're Chomsky, you'd
> say that the only possible explanation is that plants have genes
> that specify the fractal and fibonacci patterns.

Chomsky would be wrong, because genes do NOT specify phenotypes;
rather, genes are just the providers of the raw materials (i.e.,
proteins) necessary for the emergence of the phenotype (which is
many developmental levels away from the genotype). If anybody's
interested in the coaction of genes and environment, take a look
at:

Oyama, Susan, Paul E. Grifiths and Russell D. Gray (eds.)
2001 Cycles of Contingency: Developmental Systems and Evolution.
Cambridge, MA: MIT Press.

> If you're you [i.e., Jasper, and presumably Dick and me too], you'd
> say that the patterns need no explanation -- that if you apply mathematical
> methods to nature you're bound to come up with something that, superficially,
> seems systematic, but if you varied nature in random and arbitrary ways the
> same mathematical methods would still find mathematical patterns.

I would say that the Fibonacci thing is interesting, and would be
interested as to why this sort of developmental pattern is patently
successful in certain organisms but apparently not in others. I
wouldn't jump off the deep end and say that it represents perfection
or anything like that. Perfection is meaningless in evolution and
biology, because "optimality" in evolution and biology means
'satificing' (an allusion to Simon).

Joe
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